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A sharp oscillation property involving the critical Sobolev exponent for a class of superlinear elliptic problems

Published online by Cambridge University Press:  03 December 2013

Julián López-Gómez
Julián López-Gómez*
Affiliation:
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain (Lopez_Gomez@mat.ucm.es)
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Abstract

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This paper studies the asymptotic behaviour as α := u(0) ↑∞ of the first zero R(α) of the radially symmetric solution of the semilinear equation

in ℝn, n ≥ 1, where h > 0 and β > 1. We establish that R(α) = O(α−(β−1)/2) if n = 1, 2 or n ≥ 3 and β < (n + 2)/(n − 2), and conjecture that lim inf α→∞R(α) > 0 if n ≥ 3 and β > (n + 2)/(n − 2).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 143 , Issue 6 , December 2013 , pp. 1303 - 1320
Copyright
Copyright © Royal Society of Edinburgh 2013